a boat moves through the water of a river at 5.8m/s relative to the water, regardless the boat's direction. if the current is flowing at 5.04m/s, how long does it take the boat it take the boat to complete a trip consisting of a 443m displacement downstream followed by a 348m displacement upstream?

T = d1/V1 + d2/V2

T = 443/(5.8+5.04) + 348/(5.8-5.04) =
40.87 + 457.9 = 498.8 s. = 8.3 Min.

To calculate the time it takes for the boat to complete the trip, we need to consider the velocities and displacements involved.

First, let's calculate the time taken for the downstream displacement of 443m. The boat's velocity relative to the water is 5.8 m/s, and the current is flowing at 5.04 m/s. Since the boat is moving in the same direction as the current, the effective velocity of the boat for the downstream displacement is the sum of the boat's velocity and the current's velocity.

Effective velocity downstream = Boat's velocity + Current's velocity
= 5.8 m/s + 5.04 m/s
= 10.84 m/s

Now we can calculate the time taken for the downstream displacement using the formula:

Time = Distance / Velocity

Time downstream = 443 m / 10.84 m/s
≈ 40.85 seconds

Next, let's calculate the time taken for the upstream displacement of 348m. Since the boat is moving in the opposite direction of the current, the effective velocity of the boat for the upstream displacement is the difference between the boat's velocity and the current's velocity.

Effective velocity upstream = Boat's velocity - Current's velocity
= 5.8 m/s - 5.04 m/s
= 0.76 m/s

Now we can calculate the time taken for the upstream displacement using the formula:

Time = Distance / Velocity

Time upstream = 348 m / 0.76 m/s
≈ 457.89 seconds

Finally, to find the total time taken for the entire trip, we sum the time taken for the downstream and upstream displacements:

Total time = Time downstream + Time upstream
≈ 40.85 seconds + 457.89 seconds
≈ 498.74 seconds

Therefore, it takes approximately 498.74 seconds for the boat to complete the trip consisting of a 443m downstream displacement followed by a 348m upstream displacement.